Atomic fountains and optical clocks at SYRTE: status and perspectives

M. Abgrall, B. Chupin, L. De Sarlo, J. Guena, Ph. Laurent, Y. Le Coq,

R. Le Targat, J. Lodewyck, M. Lours, P. Rosenbusch, D. Rovera, and S. Bize∗

LNE-SYRTE, Observatoire de Paris, PSL Research University,CNRS, Sorbonne Universites, UPMC University Paris 06,

61, avenue de l ′Observatoire, 75014 Paris, France

In this article, we report on the work done with the LNE-SYRTE atomic clock ensemble during thelast 10 years. We cover progress made in atomic fountains and in their application to timekeeping.We also cover the development of optical lattice clocks based on strontium and on mercury. Wereport on tests of fundamental physical laws made with these highly accurate atomic clocks. Wealso report on work relevant to a future possible redefinition of the SI second.

Introduction

Research on highly accurate atomic frequency stan-dards and their applications is making fast and steadyprogress. The quest for ever increased accuracy is ad-vancing hand in hand with advances in quantum physics,with better understanding and manipulation of atomicsystems, with exploration of fundamental laws of natureand with the development of important services and in-frastructures for science and society. The quest for in-creased accuracy is also a powerful incentive to innova-tion in such areas as lasers, laser stabilization, low noiseelectronics, stable oscillators, low noise detection of op-tical signals, fiber devices and cold-atom based instru-mentation for ground or space applications. Finally, inaddition to enhancing existing applications, improved ac-curacy leads to new applications.

This article focuses on key achievements and trendsof the last 10 years. Over this period of time, the firstgeneration of laser-cooled standards, using the atomicfountain geometry, reached maturity and had large im-pact on international timekeeping. The typical accuracyof these frequency standards, 2 parts in 1016, is now per-manently accessible both locally and globally. At thesame time, a new generation of optical clocks showedtremendous and steady improvement, gaining more thantwo orders of magnitude in a decade. To date, an ac-curacy of 6.4 × 10−18 [1] was reported. Similarly, majorimprovements occurred in many other aspects of opticalfrequency metrology, notably in optical frequency combsand optical fiber links.

In this article, we will report on developments ofthe LNE-SYRTE atomic clock ensemble since our 2004report in the Special Issue of the Comptes Rendusde l’Academie des sciences on Fundamental Metrology[2]. This work exemplifies many of the above men-tioned features of research on highly accurate atomicfrequency standards. We will focus on frequency stan-dards and their impact on timescales and timekeeping, onclock comparisons, including optical-to-microwave com-parisons with combs, and their applications. Several

∗ sebastien.bize@obspm.fr

other aspects of our research are covered by other articlesof the Special Issue of the Comptes Rendus de l’Academiedes Sciences (Volume 16, Issue 5), i.e. the space missionPHARAO/ACES [3], fundamental tests with clocks [4],development of technologies for space optical clocks [5]and optical fibers links [6, 7].

1. Atomic fountains

Atomic fountains are the first generation of the laser-cooled atomic frequency standards. They use the foun-tain geometry where spectroscopy of the clock transitionis performed onto a free-falling sample of laser-cooledatoms which is beforehand launched upwards vertically(see, for instance, [8] and references therein). To date,atomic fountains using cesium provide the most accuraterealization of the SI second. One important aspect of thelast 10 years was to better understand systematic shiftslimiting the accuracy of these devices.

Distributed cavity phase shift– In atomic fountains, theRamsey interrogation is realized by the up-going anddown-going passages of the atomic sample through themicrowave Ramsey cavity. The spatial phase variationsof the field inside the cavity, when sampled by the movingatoms, induce a frequency shift, which can be describedas a residual Doppler shift. For a long time, there was alack of both a complete and agreed model for this effectand of experiments to test it. Consequently, this effectwas one of the main sources of uncertainty in atomicfountains. In [9, 10], a new approach was proposed tocompute the cavity phase distribution. We performedmeasurements of these shifts in FO2-Cs which enabledthe first quantitative comparison between theory and ex-periment [11]. This study validated the theoretical modeland lowered the distributed cavity phase uncertainty forFO2-Cs to 10−16. It also defined a method to determinethis uncertainty, which was then adopted in [12, 13] andfor other SYRTE fountains.

Microwave lensing shift– The microwave field insidethe Ramsey cavity not only excites the transition betweenthe two internal clock states but also modifies the mo-tion of atomic wave packets, leading to a frequency shift[14][15]. In [16], a new approach to compute the shift was

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FIG. 1. Overview of the LNE-SYRTE atomic clock ensemble at the Observatoire de Paris.

proposed. It was then used in a complete model of theeffect, taking into account all features of the interactionsuch as atomic velocity and space distributions and de-tection non-uniformities [12][13]. This same method wasapplied to LNE-SYRTE fountains, for which shifts arereported in table 2 of [8].

Blackbody radiation shift– In 2004, conflicting mea-surements and calculations of this shift induced by ther-mal radiation bathing the atoms were reported. This ledus to revisit our early accurate measurements of the Starkcoefficient [17]. Our new measurements at lower electricfields have been found to be in excellent agreement [18].The theory of the Stark shift developed in the 60’s turnedout to have a sign error for the tensor part. This led to asmall change of the blackbody radiation shift correctionof 7×10−17 [8]. Two independent high accuracy ab initiocalculations further agreed with the blackbody radiationshift correction derived from our Stark measurements.

Microwave leakage and synchronous phase perturba-tions– Interaction of atoms with unintended residual mi-crowave field and synchronous perturbation of phase ofthe probing field can produce shifts. We developed mi-crowave synthesizers that can be switched without intro-ducing phase transients and a phase transient analyzerwith 1 µrad.s−1 resolution [19]. Using these tools, we low-ered the uncertainty related to these putative frequencyshifts to less than 10−16.

Our approach to deal with other systematic shifts re-mained as described in our last report in the ComptesRendus [2]. Table I gives, as an example, the accuracybudget of FO2-Cs as of 2014.

Another important achievement was the simultaneousoperation with 87Rb and 133Cs of the dual fountain FO2.This was done by implementing dichroic collimators over-lapping 780 nm (for Rb) and 852 nm (for Cs) radiationsfor all laser beams, and by adopting a time sequence en-

TABLE I. Typical uncertainty budget of the FO2-Cs primaryfrequency standard (top). Uncertainty budget of the Sr1 op-tical lattice clock as of July 2011 (bottom). Tables give thefractional frequency correction and its Type B uncertainty foreach systematic shift, in units of 10−16. The total uncertaintyis the quadratic sum of all uncertainties.

FO2-Cs

Physical origin of the shift Correction Uncertainty

Quadratic Zeeman −1919.9 0.3

Blackbody radiation 168.4 0.6

Collisions and cavity pulling 201.2 1.5

Distributed cavity phase −0.9 1.2

Microwave lensing −0.7 0.7

Spectral purity & leakage 0 0.5

Ramsey & Rabi pulling 0 0.1

Relativistic effects 0 0.05

Background collisions 0 1.0

Total −1551.9 2.5

Sr1

Physical origin of the shift Correction Uncertainty

Quadratic Zeeman 19.7 0.2

Blackbody radiation 53.8 0.8

Collisions −0.2 0.5

AC Stark shift lattice 1st order −0.5 0.1

AC Stark shift Lattice 2nd order 0 0.1

DC Stark shift 0 0.01

Line pulling 0 0.5

Total 72.8 1.0

abling time resolved selective detection of the two atomicspecies [20]. Further notable improvement relates to re-liability and capability for long term unattended opera-tion. Using 2D magneto-optic traps to load the opticalmolasses suppressed residual background vapor and en-

3

hanced the lifetime of the alkali sources. Also, we devel-oped an automatic data processing system that monitorsthe status of all fountains, oscillators and internal linksin quasi real time. This system allows rapid detection offailures. It also performs automated fountain data pro-cessing, taking account of all systematic corrections, andit continuously generates frequency measurements at thenominal uncertainty of the fountains. This capability hashad major impact on timekeeping and other applicationsof atomic fountains (see sect. 4 and 5 ).

2. Optical lattice clocks

In optical lattice clocks (OLCs), a set of neutral coldatoms, dipole-trapped in an optical lattice, are interro-gated by an ultra-stable “clock” laser. Because they in-volve probing an optical transition of a large (typically104) number of tightly confined atoms, they combine anexcellent ultimate frequency stability – only limited bythe Quantum Projection Noise (QPN) – and a high accu-racy. Proposed in 2001 [21][22], OLCs made tremendousprogress in the last decade. OLCs have demonstratedunprecedented frequency stabilities of a few 10−16/

√τ

and a record accuracy below 10−17 [1], overcoming thebest ion clocks [1, 23–26]. With current improvement inlaser stabilization, OLCs are expected to reach a QPNlimited stability on the order of 10−17/

√τ within a few

years, thus enabling even better characterization of sys-tematic effects. OLCs with Sr, Yb, Hg and more prospec-tively Mg have been demonstrated. Among these atomicspecies, Sr is currently the most popular choice becauseof the accessibility of the required laser wavelengths, thepossibility to cool Sr down to sub-µK temperature usingthe narrow 1S0 → 3P1 inter-combination line, and thepossibility it offers on the control of systematic effects,most notably concerning the high order perturbation bythe trapping light and cold collisions.

Strontium optical lattice clocks– LNE-SYRTE devel-oped two OLCs using strontium atoms. The design ofthese clocks uses an optical cavity to enhance the opti-cal lattice light, giving access to large trap depths. Itenabled us to explore systematic effects induced by thetrapping laser light. These effects are specific to OLCs,and we have demonstrated that they can be controlledto better than 10−17, even with a significant trappingdepth [27, 28], thus validating the concept of OLCs. Inparticular, we have determined the precise value for the“magic wavelength” for which the impact of the trappinglight is canceled to first order, and resolved or upper-bounded a number of higher order effects. Because OLCsuse a large number of atoms in a tightly confined space,they are subject to a significant density-dependent sys-tematic frequency shift. Some groups have resolved adensity shift on the order of 10−16 with both Sr and Yb.However, the loading technique chosen at LNE-SYRTEleads to a lower atomic density, thus dramatically reduc-ing this effect below 10−17. The blackbody radiation shift

has remained the dominant contribution to the accuracybudget, with an uncertainty around 5 × 10−17 for bothSr and Yb, assuming a 1 K uncertainty on the tempera-ture of the environment. Recently, precise measurementsof the static polarizability of Yb and Sr, together withcarefully crafted environments for the atoms has enableda few groups to drastically reduce this uncertainty, downto the 10−18 range.

Comparisons between clocks are necessary to confirmtheir accuracy budget. The first comparisons betweenremote Sr OLCs were achieved by comparing to cesiumclocks (see sect. 4), but they were soon limited by thecesium accuracy. LNE-SYRTE published the first com-parison between two local OLCs that confirm the accu-racy budget of the clocks better than the accuracy ofthe cesium fountains, involving two Sr clocks with a fre-quency difference smaller than their combined accuracybudgets of 1.5 × 10−16 [23]. This resolution is obtainedafter less than one hour of integration. Table I gives theaccuracy budget of one of the Sr OLCs at the time of thiscomparison.

Mercury optical lattice clock– SYRTE also started thedevelopment of a mercury OLC. Hg has the advantageof low sensitivity to blackbody radiation and to electricfield (30 times lower than Sr, 15 times lower than Yb).For the 199Hg isotope, clock levels have a spin 1/2 forwhich the tensor light shift sensitivity is absent. Also,because of its high vapor pressure, it does not requirean oven and enables the use of a 2D magneto-optic trapas the initial source of atoms. Hg is also interesting forfundamental physics and atomic physics, because of aquite high sensitivity to a variation of α (see sect. 4) andits 7 natural isotopes. The main challenge of using Hglies in the need for deep UV laser sources. When thepotential of Hg for a highly accurate optical lattice clockarose, Hg had never been laser cooled.

In the last years, we made all the steps leading tothe demonstration, for the first time, of a Hg latticeclock. Laser cooling on the 254 nm 1S0 → 3P1 in-tercombination transition was demonstrated and stud-ied [29][30][31]. A clock laser system with thermal noiselimited instability of 4 × 10−16 was developed [32][33].We performed the first direct laser spectroscopy of thethe clock transition, firstly on atoms free-falling from amagneto-optic trap [34] and secondly on lattice-boundatoms, with linewidth down to 11 Hz (at 265.6 nm or1128 THz). We performed the first experimental deter-mination of the “magic wavelength” [35], for which ourbest value is 362.5697 ± 0.0011 nm. We performed ini-tial measurements of the absolute frequency of the 199Hgclock transition down to an uncertainty of 5.7 parts in1015 [36].

So far, the advancement of the Hg optical lattice wasmainly hindered by the poor reliability of the 254 nmlaser-cooling and by the modest lattice trap depth. Re-cent work enabled large improvements to overcome thesetwo limitations, opening the way to in-depth systematicstudies and higher accuracies.

4

3. Optical frequency combs

The development of optical frequency standards of thekind presented in the previous section is aimed at pro-ducing a laser electromagnetic field of extremely stableand accurate frequency. To realize a complete metro-logical chain that allows comparison with other stan-dards operating at different wavelengths in the opticaldomain or in the microwave domain (such as primaryfrequency standards), it is necessary to use a specific de-vice. The method of choice nowadays is the optical fre-quency comb based on mode-locked femto-second laser,that provides a phase coherent link spanning across theoptical and microwave domains. Recently, SYRTE fo-cused on a technology of comb based on erbium-dopedfiber lasers, whose foremost asset is the capability tofunction for months with a very limited maintenancewhile performing state-of-the-art measurements. Tightphase locking (bandwidth ∼ 1 MHz) of such comb onto a1.5 µm ultra-stable laser sets it in the narrow-linewidthregime where beatnotes with other ultra-stable light atother wavelengths are typically ∼ 1 Hz linewidth. Thisprovides high performance simultaneous measurementsof the various ultra-stable optical frequency references atSYRTE in the visible and near infrared domain.

The comb also behaves like a frequency divider: therepetition rate of the comb, frep, results from the co-herent division of the 1.5µm laser frequency νL. Byphoto-detecting the train of pulses and filtering out onespecific harmonic of the repetition rate, one can gener-ate a microwave signal whose phase noise is that of thecw optical reference, divided by the large frequency ra-tio (typically 20000) between a 1.5µm wavelength cwlaser and a 10 GHz microwave signal. 10 GHz signals withphase noise of -100 dBc/Hz at 1 Hz Fourier frequency and-140 dBc/Hz white noise plateau are now straightforwardto produce. This low phase noise level is comparable withthat of cryogenic sapphire oscillators and is thus suffi-cient to operate state-of-the-art microwave atomic foun-tains (sect. 1) with a short term stability limited onlyby atomic quantum projection noise. We have realizedproof-of-principle experiments of such a scheme [37] andare now progressing toward implementing it in an op-erational system. We further demonstrated several ad-vanced techniques [38–40] to reduce the imperfection ofthe frequency division and photo-detection processes. Wehave shown that it is now becoming possible to generatemicrowave signals with phase noise as low or lower thanany other technology for a large range of Fourier frequen-cies. Applications of such extremely low noise microwavesignals can be found in RADAR (civil and military) aswell as very long baseline interferometry.

Finally, the comb-based transfer of spectral purity be-tween different wavelengths recently led to exciting re-sults. This application is crucial for the future develop-ment of optical lattice clocks, whose short term stabilityis currently limited by the spectral purity of the ultra-stable clock laser probing the atomic transition. Several

competing technologies are being explored, notably atSYRTE, to improve the performance of these lasers, all ofthem very challenging, some of them wavelength-specific.Being able to utilize the performance of an extremelystable laser at a given wavelength and to distribute itsperformance to any wavelength within reach of the fre-quency comb is an important milestone for the futuredevelopments of optical lattice clocks. We demonstratedsuch transfer from a master to a slave laser with an addedinstability of no more than a few 10−18 at 1 s (see fig. 2,right), well within the requirements expected for the nextseveral years [41].

4. Fundamental physics tests

One exciting scientific application of atomic clockswith extreme uncertainties is to contribute to testing fun-damental physical laws and searching for physics beyondthe Standard Model of particle physics. The frequency ofan atomic transition relates to parameters of fundamen-tal interactions (strong interaction, electro-weak interac-tion), such as the fine-structure constant α, and to fun-damental properties of particles like for instance the elec-tron mass, me. Repeated highly accurate atomic clockcomparisons can be used to look for a putative variationwith time or with gravitational potential of atomic fre-quency ratios, and, via suitable atomic structure calcu-lations, of natural constants. Clocks provide laboratorytests, independent of any cosmological model, that con-strain alternative theories of gravity and quantum me-chanics, thereby contributing to the quest for a unifiedtheory of the three fundamental interactions.

87Rb vs 133Cs comparisons– Improvements of atomicfountains described in sect. 1 enabled major enhance-ment in the number and in the quality of Rb/Cs hyper-fine frequency ratio measurements since our last report inthe Comptes Rendus [2]. Measurements have been per-formed almost continuously since 2009. Fig.3, top showsthe temporal record of the variations of this ratio. Mea-surements extending over 14 years give stringent mea-surements of a putative variation with time and gravity ofthe Rb/Cs ratio, as reported in [42]. Taking into accountout most recent data, we get d ln(νRb/νCs)/dt = (−11.6±6.1) × 10−17 yr−1 for the time variation. For the varia-tion scaled to the annual change of the Sun gravitationalpotential on Earth U , we get c2d ln(νRb/νCs)/dU =(7.4 ± 6.5) × 10−7, which provides a differential redshifttest between Rb and Cs twice more stringent than [43].

87Sr vs 133Cs comparisons– Frequency ratios betweenoptical and microwave clocks offer a different sensitiv-ity to natural constants than hyperfine frequency ra-tios. International absolute frequency measurements ofstrontium optical lattice clocks against Cs fountain pri-mary frequency standards over a decade (fig.3, Mid-dle) give the linear drift with time of the νSr/νCs ra-tio: d ln(νSr/νCs)/dt = (−2.3 ± 1.8) × 10−16 yr−1,and of the variation with the gravitational potential:

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νS

Synthesizer

FIG. 2. Principle of the transfer of spectral purity (left): the optical beatnotes of the comb with a master laser on the onehand, and with a slave laser on the other hand, are rescaled and mixed before being compared to a stable synthesizer. Thefeedback on the offset-locked slave transfers the spectral purity of the master to the slave laser. The modified Allan deviation(right) of the noise added by the transfer itself has a level of only 2× 10−18 at 1 s, and averages down to 2× 10−20 after 1000 s.

c2d ln(νSr/νCs)/dU = (−1.3±1.5)×10−6. Because the ac-curacy of these measurements has improved considerablyover time, these bounds will be significantly improved byfuture measurements.

Combining with other comparisons– Each pair ofatoms has a different sensitivity to variations of threefundamental constants α, µ = me/mp and mq/ΛQCD.To set independent limits to variations of these threeconstants with time, one can perform weighted least-squares fit to all accurate experimental determinationsof variation with time of atomic frequency ratios, avail-able as of October 2014. This includes the above Rb/Csresult (see sect. 4), optical frequency measurements ofH(1S-2S) [45], Yb+ [46], Hg+ [47], Dy [48] and Sr (seeabove, and [23] and references therein) against Cs, andthe optical-to-optical ion clock frequency ratio Al+/Hg+

[49]. The fit yields independent constraints for the threeconstants given in the first row of the Table in fig. 3.The constraint relative to α is mainly determined by theAl+/Hg+ comparison. In this fit, only the Rb/Cs com-parison disentangles variations of µ and of mq/ΛQCD. Itis therefore essential to constrain mq/ΛQCD. This stemsfrom the fact that optical frequency measurements areall performed against the Cs hyperfine frequency, exceptAl+/Hg+.

Similarly, we perform a global analysis for the varia-tion with the gravitational potential exploiting all avail-able comparisons as of October 2014 [43, 47, 48] and theabove Rb/Cs and Sr/Cs results. The least-squares fit tothese results yields independent constraints for the threecouplings to gravity given in the second row of the Tablein fig. 3.

The number of atomic systems contributing to improvethese tests will continue to grow, e.g. with 88Sr+ [50][51]and 171Yb [52], thanks to the steady efforts of manylaboratories worldwide in the field of optical frequencymetrology.

5. Advanced timekeeping

TAI calibration with atomic fountains– The Interna-tional Atomic Time (TAI) which is based on approxi-mately 400 atomic clocks, now gets its accuracy fromsome ten atomic fountain clocks worldwide (see e.g. [53]).In the last decade, the number of calibrations of TAIwith atomic fountains has grown from approximately 10per year to 4 to 6 per month in 2014, while simulta-neously the accuracy improved from several 10−15 to afew 10−16, improving TAI a lot. Combining a tremen-dous number of monthly calibrations and a high accuracy,LNE-SYRTE atomic fountains are providing the largestcontribution to the accuracy of TAI. Between 2007 andAugust 2014, they provided 197 calibrations out of atotal of 407 calibrations worldwide, a weight of nearly50%. fig. 4, Top shows these calibrations as publishedin Circular T, and the SI second (red line) which is theaverage over all primary calibrations computed by theBIPM on a monthly basis. This illustrates how researchon laser-cooled atomic fountain started 25 years ago ledto improving an important service and infrastructure forscience and society.

UTC(OP): timescales using atomic fountain clocks–The UTC(OP) timescale, elaborated at SYRTE, in Ob-servatoire de Paris, is the real time realization of UTCfor France. It is a continuously operated time refer-ence used for multiple purposes: definition of legal timedisseminated in France, reference provided to Frenchlaboratories for synchronization applications, pivot forFrench contributions to TAI, test of advanced time trans-fer methods, link to UTC of the EGNOS system, contri-bution to the development of GALILEO, time referencefor the ground-segment of the PHARAO/ACES spacemission [54–56].

Progress in the accuracy and most importantly inthe reliability of SYRTE atomic fountains (see sect. 1)enabled a new implementation of UTC(OP). A new

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d/dt (×10−16yr−1) −0.26 ± 0.24 1.1 ± 1.4 59 ± 30

c2d/dU (×10−6) 0.27 ± 0.46 −0.2 ± 2.1 −2.9 ± 5.6

FIG. 3. Top: Temporal record of fractional variations of theνRb/νCs hyperfine frequency ratio. The error bars are thetotal 1 σ uncertainties, dominated by the systematic uncer-tainties. The solid red line is the weighted fit to a line withinverse quadratic weighting. The origin of the vertical axiscorresponds to the 87Rb secondary representation of the SIsecond recommended in 2012, with a recommended uncer-tainty 1.2 × 10−15 (grey area) [44]. Middle: Internationalcomparisons of the νSr/νCs frequency ratio. A fit shows anupper bound on a drift of this ratio, as well as on a variationsynchronized with the Earth’s orbit around the Sun. Bottom:Results of the global analysis of accurate experimental deter-minations of variations of atomic frequency ratios, availableas of October 2014. The table gives constraints on temporalvariations and on couplings to gravitational potential for thethree fundamental constants: α, µ = me/mp and mq/ΛQCD.

UTC(OP) algorithm based on a hydrogen maser steeredby the atomic fountains was developed and implementedin October 2012. The maser is predictable enough toreach a stability of ∼ 10−15. The atomic fountains allowthe maser frequency to be calibrated with an uncertaintyin the 10−16 range [8, 57]. These features are sufficientto maintain a phase deviation of a few ns over 1 − 2months, which corresponds to the delay of publication ofthe BIPM Circular T. This timescale is as autonomous

and independent as possible, except a small long termsteering to remain close to UTC, and does not rely onany other timescale available in real time such as GPStime or other UTC(k). A timescale with these charac-teristics provides a powerful tool to understand currentlimits and eventually improve international timekeeping.

Practically, UTC(OP) is realized using a microphasestepper fed by the reference maser. A frequency cor-rection is updated every day to compensate the maserfrequency and maintain UTC(OP) close to UTC. Thiscorrection is the sum of two terms. The main term cor-responds to the current frequency of the maser as mea-sured by the fountains. The value is estimated with a lin-ear extrapolation of the data covering the past 20 daysto remain robust against possible interruptions of dataprovision or of the automatic data processing. The sec-ond term is a fine steering to maintain UTC(OP) close toUTC, compensating the frequency and phase offset be-tween UTC(OP) and UTC. It is updated monthly at theBIPM Circular T publication. The steering correction isusually of the order of 10−15 or below.

Figure 4, bottom presents the comparison of threeUTC(k) to UTC as published in Circular T since theimplementation of the new UTC(OP). Over this pe-riod, UTC(OP) is one of the 3 best real time realiza-tions of UTC [58, 59], with UTC(PTB), the pivot oftime transfers for international contributions to TAI, andUTC(USNO), the laboratory providing the largest num-ber of clock data included in EAL computation. De-parture between UTC(OP) and UTC remains well below10 ns, with a rms value less than 3 ns. This is an improve-ment of about a factor of 5 compared to the previous real-ization method of the timescale. On-going instrumentalupgrades shall further improve the short term stabilityof the timescale and the robustness of the system.

6. Toward a redefinition of the SI second

Several optical frequency standards are now largelysurpassing Cs atomic fountains which realize the secondof the international system of units (SI) and define theaccuracy of TAI. This opens the inviting prospect of aredefinition the SI second. In 2001, anticipating this sit-uation, the Consultative Committee for Time and Fre-quency (CCTF) of the Comite International des Poids etMesures (CIPM) recommended that a list of SecondaryRepresentations of the Second be established. SecondaryRepresentations of the SI Second (SRS) are transitionswhich are used to realize frequency standards with ex-cellent uncertainties, and which are measured in the SIsystem with accuracies close to the limit of Cs fountains.They are part of the broader list of recommended valuesof standard frequencies produced and maintained by theCCL-CCTF Working Group and adopted by the CIPM.Producing and maintaining these lists of recommendedvalues is a vehicle to keep track of measurements provid-ing the most stringent connections between the optical

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FIG. 4. Top: Calibrations of TAI by the atomic fountainPFSs. Filled symbols: contributions of SYRTE fountains.Solid red line: the SI. Bottom: Comparisons of 3 UTC(k)to UTC: UTC(OP), UTC(PTB) and UTC(USNO). The in-set shows the significant improvement achieved with the newmethod for generating UTC(OP) implemented at MJD 56218,compared to the previous one using a commercial Cs clockmanually steered towards UTC.

domain and the SI second, and to verify the level of con-sistency between these measurements. This is an impor-tant task to prepare for a possible redefinition of the SIsecond.

Contributions to the list of recommended values– LNE-SYRTE provided several high accuracy absolute fre-quency measurements which contributed to the list ofrecommended values. The 87Rb hyperfine transitionwas measured repeatedly against Cs fountains, as al-ready shown in fig. 3. This transition became the firstSecondary Representation of the Second proposed bythe CCTF in 2004, based our early measurements, andadopted by the CIPM in 2006. After further significantprogress visible in fig. 3, the recommended value was re-vised by the 2012 CCTF and adopted in 2013. The ori-gin of the vertical scale of the graph is the recommendedvalue of 2012 and the gray area represents the recom-mended uncertainty. The weighted average of all datapoints (green line) gives (2.15 ± 1.48) × 10−16 is consis-

tent with zero within the smallest overall uncertainty ofthe measurements (4.4× 10−16). LNE-SYRTE also pro-vided absolute frequency measurements that contributedto the establishment of the recommended values for the1S0 → 3P0 of 87Sr [60], 88Sr [61] and 199Hg [36]. Usingthe transportable Cs fountain primary standard FOM,LNE-SYRTE also contributed to the establishment of therecommended value for H(1S-2S) (measured at the MaxPlanck Institut fur Quantenoptik, Garching, Germany)[62] and 40Ca+ (at the University of Innsbruck, Austria)[63].

87Sr is currently the most widespread optical frequencystandard. For this reason a large number of groups mea-sured the absolute frequency of 87Sr against Cs with aremarkable degree of consistency, as can be seen in fig. 3,middle. These measurements led the 2006 CCTF to rec-ommend the 87Sr as a Secondary Representation of theSI second. The recommended value was updated by the2012 CCTF based on measurements from 5 institutes. Ithas a recommended uncertainty of 1 × 10−15. More re-cently, LNE-SYRTE reported a measurement of the 87Srclock transition with an uncertainty of 3.1×10−16 limitedby the accuracy of atomic fountains [23]. This is the mostaccurate absolute measurement to date of any atomic fre-quency. One of the key factors for the measurement isthe record stability between an optical and a microwaveclock: 4.1 × 10−14/

√τ against Cs (and 2.8 × 10−14/

√τ

against Rb). In 2014, PTB reported another absolute fre-quency measurement with an uncertainty of 3.9× 10−16

[25]. These two last measurements are in excellent agree-ment.

Using a Secondary Representation of Second to cali-brate TAI – One major application of primary frequencystandards is to calibrate and steer the scale interval ofthe widely used International Atomic Time TAI. It is im-portant to anticipate how a possible redefinition of thesecond would impact the elaboration of TAI. We used theFO2-Rb fountain to investigate how a Secondary Repre-sentation of Second could participate to TAI. Calibra-tions of the frequency of our reference hydrogen maserwere produced with FO2-Rb, in a similar way that abso-lute calibrations are done with primary frequency stan-dards. These data were then submitted to the BIPM andto the Working Group on Primary Frequency Standards.Following this submission, the BIPM and the WorkingGroup defined how frequency standards based on Sec-ondary Representations will be handled by the BIPMand how they will be included into the Circular T. TheWorking Group was renamed Working Group on Primaryand Secondary Frequency Standards and it was decidedthat calibrations produced by LNE-SYRTE with FO2-Rbcould be included into Circular T and, since July 2013,contribute to steering TAI. This was the first time thata transition other than the Cs hyperfine transition wasused to steer TAI [57].

Absolute frequency measurement against the TAI en-semble– More than 40 formal calibrations of TAI withFO2-Rb have been sent, processed by the BIPM and pub-

8

lished into Circular T. These data can be used to measurethe frequency Rb hyperfine transition directly against thesecond as realized by the TAI ensemble. This can bedone with a statistical uncertainty of 1 part in 10−16,and therefore at the accuracy limit of primary frequencystandards defining the scale interval of TAI [57]. This il-lustrates how TAI provides worldwide access to the accu-racy of Cs fountains. This also shows how recommendedvalues of Secondary Representation of the Second basedon optical transitions could be checked against the SIsecond as realized by the TAI ensemble.

7. Prospects

In the future, highly accurate atomic clocks and theirapplications will keep improving at a high pace. An im-portant milestone in the field will be the simultaneousavailability of advanced timescales, of the new gener-ation of optical clocks and of the means to comparedthem remotely at unprecedented levels of uncertainty. Inthe coming decade, the ACES mission will allow ground-to-space comparisons to the 10−16 level and ground-to-ground comparisons to the mid 10−17 level [3]. Opticalfiber links will allow comparisons of the most accurateoptical clocks at their limit: 10−18 or better [6, 7]. Wecan confidently predict major improvements in all ap-plications of highly accurate atomic clocks. Availabil-ity of clocks and clock comparisons at the 10−18 level

can further enable new applications. Clock comparisonsdetermine Einstein’s gravitational redshift between the2 remote clock locations. For a clock at the surface ofthe Earth, 10−18 corresponds to an uncertainty of 1 cmin height-above-geoid, making the idea of clock-basedgeodesy realistic and potentially useful. Highly accurateclocks could become a new type of sensors for applica-tions in Earth science, illustrating once again the fertil-izing power of the quest for ever increased accuracy.

Acknowledgements

SYRTE is UMR CNRS 8630 between Centre Nationalde la Recherche Scientifique (CNRS), Universite Pierre etMarie Curie (UPMC) and Observatoire de Paris. LNE,Laboratoire National de Metrologie et d’Essais, is theFrench National Metrology Institute. SYRTE is a mem-ber of IFRAF, of the nanoK network of the Region Ile deFrance and of the FIRST-TF LabeX. We acknowledge thelarge number of contributions of SYRTE technical ser-vices. This work is supported by LNE, CNRS, UPMC,Observatoire de Paris, IFRAF, nanoK, Ville de Paris,CNES, DGA, ERC AdOC, EMRP JRP SIB55 ITOC,EMRP JRP EXL01 QESOCAS. We are grateful to theUniversity of Western Australia and to M.E. Tobar forthe long-lasting collaboration which gives us access tothe cryogenic sapphire oscillator used in the LNE-SYRTEultra-stable reference.

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